Having completed this module, you should be able to:
A1 Define the terms that are emboldened and flagged in the margins of this module.
A2 Recognize the circumstances in which electromagnetic induction occurs and explain, qualitatively, the operation of devices that use it.
A3 Use Lenz’s law to determine the polarity of an induced voltage and the direction of an induced current. A4 Calculate the magnetic flux linkage in a circuit.
A5 Use Faraday’s law of electromagnetic induction to deduce the magnitude of an induced voltage. A6 Deduce magnetic field strength from experiments with a search coil.
A7 Apply the relationships between voltage, current and numbers of turns in the primary and secondary coils of a transformer.
A8 Explain the action of an inductance in a circuit
A9 Calculate coefficients of self and mutual inductance for solenoids.
A10 Derive and apply the relationship between the induced voltage in a moving wire, the local magnetic field strength and the wire’s velocity.
A11 Show that Faraday’s law of electromagnetic induction is consistent with the Lorentz force on a conduction charge in a moving wire.
A12 Determine the polarity of the voltage induced and the direction of the current induced in a wire which is moving through a magnetic field.
A13 Explain the principles of an alternator (and how it can be modified to make a d.c. dynamo) and of a homopolar generator.
A14 Explain the origin of eddy currents and appreciate some of their uses and disadvantages.
Study comment You may now wish to take the Exit test for this module which tests these Achievements. If you prefer to study the module further before taking this test then return to the Module contents to review some of the topics.
6.3 Exit test
Study comment Having completed this module, you should be able to answer the following questions, each of which tests one or more of the Achievements.
☞
output
coil with many turns iron core
magnetic tape (arrows indicate strength and direction of field within tape)
motion of tape
Figure 234See Question E1. Question E1
(A2)4Figure 23 is a schematic diagram of the playback head in a tape recorder. Information is stored on the tape in the form of a magnetic field pattern (possibly produced by the output from a microphone). Explain what happens to the output voltage as the tape moves past the head.
Question E2
(A2, A3, A5, A12 and A13)4Figure 11 shows a simple alternator and Figure 13 shows the total flux linkage as the coil turns.
S N rotation r2 r1 slip rings brushes P Q
Figure 114A simple alternator. 0
90° 180° 270° 360° θ Φ
Figure 134The flux linkage changes as the alternator coil rotates.
S N rotation r2 r1 slip rings brushes P Q
Figure 114A simple alternator. If a particular coil makes one full rotation every
401ms and the voltage output oscillates between ±11V:
(a) Sketch a graph of the output voltage for two full cycles.
(b) Explain how Lenz’s law and the Lorentz force can each be used to find the direction of the induced current when the coil is moving through the position shown in Figure 11.
(c) On your sketch from (a) show how the output will change if the rotation frequency of the coil is doubled.
R
circular cross section, radius r N turns
Figure 244See Question E3. Question E3
(A4, A5 and A9)4Figure 24 shows a toroidal solenoid. The magnetic field strength at each point on the circular axis of the ring is given by B = µ0NI/(2πR).
(a) If R = 1.01m, N = 201000 turns, I = 1.01A and the circular cross section of the toroid has a radius r = 2.01cm, calculate the magnetic flux crossing a section of the toroid. (Assume the magnetic field strength B to be uniform across the section.)
(b) If the current in the solenoid grows at the rate of 121A1s−1 calculate the voltage induced in one turn of the solenoid.
(c) Calculate the total induced voltage in the solenoid. (d) Calculate the total coil inductance L0.
Question E4
(A4 and A6)4In an early experiment to measure the strength of the Earth’s magnetic field, a large flat vertical coil of 400 turns and radius 301cm, with its axis pointing to magnetic north, was turned through 180° about a vertical diameter. The coil was connected to a ballistic galvanometer which measured a charge flow of 49.21µC when the coil was turned round. The total resistance of the circuit was 2001Ω0.
(a) Calculate the magnitude Bh of the horizontal component of the Earth’s magnetic field strength.
(b) How should the coil be positioned and turned to measure the vertical component of the Earth’s magnetic field strength?
R
circular cross section, radius r N turns
Figure 244See Question E3. Question E5
(A7 and A9)4A ring-shaped transformer consists of a primary coil of 12 turns1cm−1 and cross-sectional area 6.01cm2, wound completely around the ring (as in Figure 24) with a superimposed secondary coil of 3000 turns in total, also wound completely around the ring. The ring has radius R = 151cm and the material of the core has relative permeability µr= 500. Assume this transformer to be ‘ideal’.
(a) If there is an alternating voltage of 2401V across the primary coil, what is the output voltage from the secondary?
(b) How could this transformer be used to step down an a.c. voltage of 2401V, and what would then be the output voltage?
Question E6
(A8 and A14)4A coil of several hundred turns is wound on to a solid iron core. When the coil is connected in series with a lamp and a 121V battery, the lamp glows brightly. When the same lamp and coil are connected to a 121V a.c. supply, (a) the lamp barely glows at all and (b) the coil becomes very hot. Suggest an explanation for each of the observations (a) and (b).
Study comment This is the final Exit test question. When you have completed the Exit test go back to Subsection 1.2 and try the Fast track questions if you have not already done so.
If you have completed both the Fast track questions and the Exit test, then you have finished the module and may leave it here.